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Page 3
... Mechanics 145 175 218 The Ergodic Hypothesis : A Complicated Problem of Mathematics and Physics by Adrian Patrascioiu 263 The FPU Problem : Excerpts from " Studies of Nonlinear Problems " by Fermi , Pasta , and Ulam Does Equipartition ...
... Mechanics 145 175 218 The Ergodic Hypothesis : A Complicated Problem of Mathematics and Physics by Adrian Patrascioiu 263 The FPU Problem : Excerpts from " Studies of Nonlinear Problems " by Fermi , Pasta , and Ulam Does Equipartition ...
Page 13
... mechanics - such ergodic be- havior is the rule ... It took us more than two years to break through and to finish a long paper , which appeared in The Annals of Mathematics in 1941 and which I consider one of the more im- portant ...
... mechanics - such ergodic be- havior is the rule ... It took us more than two years to break through and to finish a long paper , which appeared in The Annals of Mathematics in 1941 and which I consider one of the more im- portant ...
Page 15
... mechanics , large - scale motion problems , hydro- dynamics , behavior of radiation ... Compared to quantum theory the project work was like applied mathematics as compared with abstract mathe- matics . [ Edward ] Teller , in whose ...
... mechanics , large - scale motion problems , hydro- dynamics , behavior of radiation ... Compared to quantum theory the project work was like applied mathematics as compared with abstract mathe- matics . [ Edward ] Teller , in whose ...
Page 17
... mechanics of con- tinua . [ Both ideas required extensive machine computation . ] MADE IN USSR Computing machines came about through the confluence of scientific and technological devel- opments . On one side was the work in mathe ...
... mechanics of con- tinua . [ Both ideas required extensive machine computation . ] MADE IN USSR Computing machines came about through the confluence of scientific and technological devel- opments . On one side was the work in mathe ...
Page 32
... mechanics . I turned around , surprised at the thoroughness of his knowledge , and he smiled . But a few minutes later he again fell silent , and the gloom started all over . After a pause that was undoubtedly longer than he could bear ...
... mechanics . I turned around , surprised at the thoroughness of his knowledge , and he smiled . But a few minutes later he again fell silent , and the gloom started all over . After a pause that was undoubtedly longer than he could bear ...
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Popular passages
Page 299 - Talibus orabat dictis, arasque tenebat, cum sic orsa loqui vates : ' Sate sanguine divom, 125 Tros Anchisiade, facilis descensus Averno ; noctes atque dies patet atri janua Ditis ; sed revocare gradum superasque evadere ad auras, hoc opus, hie labor est.
Page 231 - But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.
Page 210 - The low-velocity equation of state for a lattice gas can be written as p - ^p (l - |v2), where p is the pressure, p is the density, and v is the flow speed.
Page 316 - Southeastern Conference on Combinatorics. Graph Theory, and Computing (Florida Atlantic University, Boca Raton, Florida, April 2-6, 1979), 3-18.
Page 121 - He is a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Physical Society and the American Association for the Advancement of Science.
Page 231 - A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws...
Page 224 - Instead, we conclude by remarking that really efficient high-speed computing devices may, in the field of non-linear partial differential equations as well as in many other fields, which are now difficult or entirely denied of access, provide us with those heuristic hints which are needed in all parts of mathematics for genuine progress.
Page 272 - Let us say here that the results of our computations show features which were, from the beginning, surprising to us. Instead of a gradual, continuous flow of energy from the first mode to the higher modes, all of the problems show an entirely different behavior.
Page 58 - That was dramatized by Bertrand, who considered the problem of finding the probability that a chord of a circle chosen "at random" be longer than the side of an equilateral triangle inscribed in the circle.